ME250 F22 Final Exam

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University of Michigan *

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250

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Mechanical Engineering

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Feb 20, 2024

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ME250 F22 FINAL ASSESSMENT This is an open-book exam. You may NOT consult any resources outside of your ME250 lecture notes, your HW, and any other resources posted on the ME250 F22 Canvas site. You should have paper (or a tablet computer) for writing, pencil, calculator, and a way to upload your solutions. Only if you have a question during the exam, use this Zoom link to ask for clarification: https://umich.zoom.us/j/99974595723 The 1:30pm-3:30pm exam time slot includes time for upload. Make sure to start uploading your exam to Gradescope with at least 5 minutes left. The Gradescope exam assignment will let you upload your exam up to 1 hour late, so do NOT email your late submission. Exams uploaded late WILL face stiff penalties, including potential non-acceptance of the submission (0% score), unless proof you completed the work on time is provided in extenuating technical circumstances. You can provide proof of extenuating circumstances via an email to me250F22instructors@umich.edu or via phone (734 615 4244) in a real time emergency. The Honor Code is on the last page of this exam.

Question 1 (13 points) Sam decides to electrify a Radio Flyer Classic red wagon to carry materials from GGB to Chrysler for lecture. He will power it using a 12V ATV battery and a DC electric motor with the following torque/speed and power/efficiency curves: A. (2 points) What are the stall torque, , stall current, , no-load speed, , and no-load current, 𝑇 ? 𝐼 ? ? 0 𝐼 0 ? Use the units provided in the plots. B. (1 point) At what torque, , is the motor most efficient? What is the power output, , of the 𝑇 ??? 𝑃 ??? motor when operating at ? How fast, , is the motor spinning at ? How much current, 𝑇 ??? ? ??? 𝑇 ??? , is the motor drawing at ? Use the units provided in the plots. 𝐼 ??? 𝑇 ???

C. (4 points) Sam realizes that the resistance of the wires causes the voltage to drop, so he scales down his motor curves to a lower operating voltage. At peak efficiency, his motor torque is now = 55 N-mm. Sam also uses a force gauge to measure the average force required to pull the 𝑇 ??? cart from GGB to Chrysler and back. The average force is = 5N, the diameter of his driven 𝐹 𝑎𝑣? wheel is D = 0.1m, and the gear-to-gear efficiency for each gear mesh of his gear train is η = 0.9. Gear 1 is on the motor shaft, Gears 2 and 3 are rigidly connected on an idler shaft, and Gear 4 is on the driven wheel shaft. If Sam wants to size Gear 4 so that the motor is operating at peak efficiency, what should be Gear 4’s tooth count, diameter, diametral pitch, and pressure angle?

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D. (4 points) Sam takes a closer look at his data and finds that the force required to pull the cart peaks when moving over bumps in building entrances. Specifically, he sees a maximum force required = 17.5N. Gear 1 is on the motor shaft, Gears 2 and 3 are rigidly connected on an 𝐹 ?𝑎? idler shaft, and Gear 4 is on the driven wheel shaft. If Sam’s stall torque at the decreased voltage is = 300 N-mm, and he wants to use a safety factor of 2 for this worst case, what should be 𝑇 ? Gear 4’s tooth count, diameter, diametral pitch, and pressure angle?

E. (2 points) Which Gear 4 should Sam use, the one from part C or the one from part D, to ensure the cart makes its trip? Justify your answer.

Question 2 (14 points) Length of wheelbase (L wheelbase ) 1.0 m Radius of wheels (R wheel ) 50.0 mm Thickness of carriage (y carriage) 5.0 mm Height of weight from axis of wheels (h weight ) 100.0 mm Second moment of area of carriage (I) 1000 mm 4 Modulus of Elasticity of carriage material (E) 200 GPa Yield strength of carriage material ( 𝜎 y ) 300 MPa Motor Torque (T motor) 10 N-m A. (3 points) Cam gives you his little blue wagon and asks you to run some calculations for him so he can beat Ohio State’s little red wagon. For starters, he asks you some structural questions. Assume the weight of the carriage and the wheels is negligible compared to the added weight, and use g = 10 m/s 2 . a. Calculate the maximum possible weight P in Newtons the carriage can support in the center without yielding of the carriage if you assume the carriage acts as a simply supported beam. Use the provided information about the wagon in the table above. Hint: where , σ ?𝑎? = ? ?𝑎? *? ?𝑎? 𝐼 ? ?𝑎? = ? 𝑐𝑎??𝑖𝑎?? 2 ? ?𝑎? = 𝑃? 4

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B. (8 points) You have one motor that can provide 10 N-m of torque that you can use to add power to the wagon, and decide to place the motor on one of the rear wheels. Cam tells you that the wagon unfortunately has no brakes, so you need to make sure the wagon with the weight can stop on a downward sloping ramp without moving. Assume the added weight does not slip on the carriage of the wagon. a. In order to accommodate the motor, you need to machine a new shaft for the wheel that the motor can connect to. i. Name at least one mechanical element that you could use to connect the motor shaft to the shaft of the wheel. ii. Name at least one mechanical element you could use to prevent the wheel from moving axially along the shaft. b. One of the requirements is that the wagon must be able to stop on the incline of 15 degrees with the weight you calculated in part A rigidly attached to the center of the carriage, as drawn above. What coefficient of friction is needed between the driven wheels and the ramp that allows the motor to prevent the blue wagon from traveling down the slope? Give your answer to two decimal places. Note: if you were unable to find the maximum weight in part A, make a note of this and use 500 N. C. (3 points) In reality, the coefficient of friction is too low to prevent slippage. Suggest 3 ways you could improve the ability of the wagon to stay parked on higher ramp angles. Be creative, there are many possibilities!

Question 3 (16 points) Dom misses the authentic tacos and burritos from California and the Qdoba on North Campus closed so she decides to make a startup called DroneThrown that makes and delivers tacos and burritos via drones. DroneThrown makes one type of burrito and two types of tacos in house, packages them, and then delivers them via drones to hungry engineering students Once the order has been received, the food preparation starts with tortilla dough preparation (Production rate = 400 orders/hr) and then continues with a cutting station that cuts the dough to the appropriate size (Production rate = 600 orders/hr) . After the cutting station, the line splits into a filling station for tacos and a filling station for burritos - The filling station for tacos continues straight from the cutting station (Production Rate = 200 orders/hr) where the tacos are filled with toppings. - The filling station for burritos continues from the cutting station (Production rate = 100 orders/hr) . The burritos then advance to a wrapping station (Production rate = 100 orders/hr ) where the burritos are completed. Then the two lines reunite and then get packaged at a packaging station (Production rate = UNKNOWN orders/hr) .The food is loaded onto the drone and then delivered (Production rate = 50 orders/hr) . A. (5 points) Draw a functional diagram of the flow lines for taco and burrito production and drone deployment. Identify known + unknown production rates for each block. B. (2 points) What is the smallest production rate for the packaging station for it to not be the bottleneck of the DroneThrown operation?

C. (3 points) Assume that the production rate for the packaging station was found to be 400 orders/hour. After six months of operation, the DroneThrown operation is running smoothly with all machines operating without any breakdowns. However, the system is unable to keep up with the numbers of order. Identify the bottleneck of the system and suggest two ways how the productivity of the Drone Thrown operation could be increased assuming perfect reliability of the machines. D. (4 points) In reality, the DroneThrown system operators find that the blades on the cutting machine often become dull and need replacing, which requires the cutting machine to stop operating for 30 minutes. Which, if any, machines would be starved, and which, if any, would be blocked? You have a spare empty table in the facility which you could use to store partly made food. Where would you put it to minimize the effect of cutting machine maintenance on the overall productivity of DroneThrown? How many food items would you want to store on the table so that productivity will be unaffected by cutting machine downtime? E. (2 points) Assume the production rate of the packaging station is 400 orders/hr. The business department at DroneThrown calculates a system Takt time of 60 seconds. Is DroneThrown able to satisfy demand for its tasty food assuming normal operation? Hint: find the cycle time of the system (which is 1/production rate)

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Question 4 (13 points) Pictured is a series of products made using one of the manufacturing processes discussed in this course. Indicate which primary shaping process(es) were used to make the products and justify your answer. A. (2 points) Metal cheese grater (excluding the handle) B. (2 points) Lightweight, non-hollow, plastic lawn chairs

C. (2 points) Plastic gallon jug for milk (excluding the cap)

D. (4 points) The iPhone 4 is made of an assembly of stamped/bent steel sheet metal and machined pieces, whereas the iPhone 6 is entirely made of aluminum. What is the manufacturing process used to make the iPhone 6 metal housing? Also, what is one tradeoff in manufacturability compared to the iPhone 4 housing? iPhone 4 housing is shown above

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iPhone 6 metal housing is shown above E. (3 points) Explain the necessity of a draft angle in many manufacturing processes and its particular importance when making parts made from a liquid material

Question 5 (11 points) It’s the holiday season and you work for a manufacturer that is considering purchasing a new process line for making holiday lights. The Bright-Line-XXL process chain has an upfront investment cost of $100000, annual maintenance that occurs at the end of each year that costs $5000, and an expected lifespan of 5 years. After 5 years, when the equipment is replaced, there are no maintenance costs but a $5000 charge to manage end-of-life disposal and recycling of the machines. The value of the sales generated by the machine is estimated to be $30000 per year, which can be assumed to occur at the end of the year during which the sales are made. (a) (3 points) What is the net present value of this investment? Assume a discount rate of 15% (b) (2 points) Is the internal rate of return on the Bright-Line-XXL greater or less than 15% and why? (c) (4 points) New management comes in and the company instead invests in the Light-up-your-life process chain and trial production begins. The design specification for the lights states that (when powered by a standard 110 V supply) each light should provide between 700 and 750 lumens. One hundred lights from the new process line are tested and found to have a mean of 717 lumens and a standard deviation of 5 lumens. Calculate the Cp and Cpk (d) (2 points) After careful adjustment of machine settings, a new batch of samples shows an updated mean of 725 lumens and a standard deviation of 4 lumens. Is this a six-sigma manufacturing system and why/why not?

Question 6: Honor Code “I have neither given nor received aid on this exam, nor have I concealed any violation of the honor code.” Signature: ________________________________________

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